ex7.c

multipleshooting to find the roots of the non-linear functions

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "math_util.h"
main()
{
   FILE *output_file, *input_file;
   int n, m, ms, i, j, k, ierr;
   long double tend, **yout, **zout, *time, tol;

   void dyn( long double *, long double *, long double *, long double * );
   void dynjac( long double *, long double *, long double **, 
                long double **, long double **, long double ** );
   void dynbc( long double *, long double *, long double * );
   void dyndbc( long double *, long double *, long double **, 
                long double ** );
   int mshoot_dae( long double **, long double **, long double *, int, 
                   int, int, long double, 
                   void(*)(), void(*)(), void(*)(), void(*)() );
   
   n = 4;
   m = 1;
   ms = 21;
   time = a1d_allo_dbl( ms );
   yout = a2d_allo_dbl( ms, n );
   zout = a2d_allo_dbl( ms, m );
   tol = 1.0e-4;
   tend = 1.0;
   
   output_file = fopen("ex7.dat","w");
   if( output_file == NULL ) {
      printf("ERROR unable to open output file\n");
      exit(1);
   }

   for( i = 0; i < ms; i++ ) {
      time[i] = i*tend/(ms-1);
      yout[i][0] = 0.0;
      yout[i][1] = 1.0;
      yout[i][2] = 1.0;
      yout[i][3] = 2.0;
      zout[i][0] = 0.1;
      printf("%Le %Le %Le %Le %Le %Le\n",time[i],yout[i][0],
             yout[i][1],yout[i][2],yout[i][3],zout[i][0]);
   }

   ierr = mshoot_dae( yout, zout, time, n, m, ms, tol, dyn, dynjac, dynbc, 
                      dyndbc );

   for( i = 0; i < ms; i++ ) {
      fprintf(output_file,"%Le\t",time[i]);
      for( j = 0; j < n; j++ )
         fprintf(output_file,"%Le\t",yout[i][j]);
      for( j = 0; j < m; j++ )
         fprintf(output_file,"%Le\t",zout[i][j]);
      fprintf(output_file,"\n");
   }
    
   fclose( output_file );    
}
void dynbc( sy0, syms, r )
long double *sy0, *syms, *r;
{
   extern long double alpha;
   r[0] = sy0[0];
   r[1] = sy0[1];
   r[2] = syms[0]-2.0;
   r[3] = syms[1]-2.0;
}
void dyndbc( sy0, syms, a, b )
long double *sy0, *syms, **a, **b;
{
   extern long double alpha;
   mat_null( a, 4, 4 );
   mat_null( b, 4, 4 );
   a[0][0] = 1.0;
   a[1][1] = 1.0;
   b[2][0] = 1.0;
   b[3][1] = 1.0;
}
void dyn( y, z, f, g )
long double *y, *z, *f, *g;
{
   f[0] = y[1];
   f[1] = -y[0]+(1.0-y[0]*y[0])*y[1] + z[0];
   f[2] = -2.0*y[0]+y[3]+2.0*y[0]*y[1]*y[3];
   f[3] = -y[1]-y[2]-y[3]*(1.0-y[0]*y[0]);
   g[0] = y[3]+z[0];
}
void dynjac( y, z, fy, fz, gy, gz )
long double *y, *z, **fy, **fz, **gy, **gz;
{
   int n = 4, m = 1;   
   mat_null( fy, n, n );
   mat_null( fz, n, m );
   mat_null( gy, m, n );
   mat_null( gz, m, m );
   fy[0][1] = 1.0;
   fy[1][0] = -1.0-2.0*y[0]*y[1];
   fy[1][1] = 1.0-y[0]*y[0];
   fy[2][0] = -2.0+2.0*y[1]*y[3];
   fy[2][1] = 2.0*y[0]*y[3];
   fy[2][3] = 1.0+2.0*y[0]*y[1];
   fy[3][0] = 2.0*y[0]*y[3];
   fy[3][1] = -1.0;
   fy[3][2] = -1.0;
   fy[3][3] = 1.0-y[0]*y[0];
   fz[1][0] = 1.0;
   gy[0][3] = 1.0;
   gz[0][0] = 1.0;
}